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Math Help - [SOLVED] Cubic Functions, quick question. Please help :)

  1. #1
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    Exclamation [SOLVED] Cubic Functions, quick question. Please help :)

    I was assigned a project from my online algebra II class and I've done the project and answered most of the questions but I'm stuck on a few of them that aren't really explained in my lesson. Would really appreciate any help.

    As reference here is the assignment:
    Equipment
    Graphing Tool (provided), 8 pieces of 8.5 x 11 paper, Scissors, Ruler, Tape, Pencil

    Procedure
    1. Cut each of the 8 pieces of paper into squares measuring 8 inches by 8 inches.
    2. Using a pencil and ruler, mark each side off in 1/2 inch increments so that you have created a piece of graph paper that has
    16 squares by 16 squares. Repeat this procedure for all 8 pieces of paper.
    3. Take one sheet of graph paper and cut out one square out of each of the 4 corners. Fold up the 4 sides to create a box
    (without a lid) that has 14 squares across the bottom and has a height of 1 square up. You may want to tape the sides in
    place. This is your first of 8 boxes.
    4. Repeat step #3 cutting 1 inch squares from each of the 4 corners and folding up the sides. Continue with the remaining 6
    pieces of paper increasing the size of the squares that you will cut out by 1/2 inch. Can the last piece of paper have 4 inch
    squares cut from each corner? Why or why not?
    5. Create a data table like the example data table below.
    Note: The measurements are in inches, not squares. Each square is 1/2 inch. Volume should be given in cubic inches.

    ----------------------------------------------------------------------------
    QUESTION:
    I have done the data table and don't need help with that however these are the questions I'm stuck on.

    5. Where does your function graph intersect the x-axis? These points are called the zeros of the function. Notice that you are able to see the zeros in the graph of the function but not in the graph of your actual data points. What is the reason for that? Think about the differences between real data and the graph of an equation.

    I said that the graph intersects at (0,0) [Link to the graph I made: http://i43.tinypic.com/2ir3v5j.png] but I don't understand how to explain the reason why and where I can go to find out about how to determine that.

    2nd Question: What does the highest point of a cubic graph represent?


    Again I would really appreciate any help. Thanks in advance!
    Last edited by amisunshinee; March 23rd 2010 at 06:06 AM.
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  2. #2
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    Also if it helps here is my data:
    Box Number: 1, 2, 3, 4, 5, 6, 7
    Length (in.): 7, 6, 5, 4, 3, 2, 1
    Width (in.): 7, 6, 5, 4, 3, 2, 1
    Height (in.): 0.5, 1, 1.5, 2, 2.5, 3, 3.5
    Volume (cu. in.): 24.5, 36, 37.5, 32, 22.5, 3.5

    (Link if the format confuses anyone: http://i44.tinypic.com/2zyy910.png)
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  3. #3
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    Hello amisunshinee

    You don't tell us what function you got for the volume, but I assume that you got:
    V = x(8-2x)^2, where x is the height of the box.
    QUESTION:
    I have done the data table and don't need help with that however these are the questions I'm stuck on.

    5. Where does your function graph intersect the x-axis? These points are called the zeros of the function. Notice that you are able to see the zeros in the graph of the function but not in the graph of your actual data points. What is the reason for that? Think about the differences between real data and the graph of an equation.

    I said that the graph intersects at (0,0) [Link to the graph I made: http://i43.tinypic.com/2ir3v5j.png] but I don't understand how to explain the reason why and where I can go to find out about how to determine that.
    Your graph is fine. But you'll see that there are two points where the graph meets the x-axis. The other one is (4,0).

    I think you're perhaps thinking that this is a harder question than it really is. The reason you can't see the zeros in the graph of your actual data is simply that you can't make a box that has either zero height ( x = 0) or zero cross-sectional area ( x = 4).

    So in the graph of an equation, we may have values of x that are not possible to obtain in practice.


    2nd Question: What does the highest point of a cubic graph represent?
    The highest point on the graph of your data (which occurs at approximately x = 1.3) represents the greatest volume that can be achieved using this size sheet of paper. That maximum volume is approximately 38\text{ cm}^3.

    Grandad
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  4. #4
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    Thank you, I was over thinking it actually. You were a great help.
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